Rapid solution of integral equations of scattering theory in two dimensions (Q1262727)

The author considers the two-dimensional problem of scattering by a homogeneous obstacle. He points out that the problem, originally expressed in terms of the Helmholtz equation, can be reformulated in integral equation form. He discusses the error in the truncation of infinite series of Bessel functions and develops an iterative algorithm for solving the integral equation system. He indicates that, when these are n nodes, the amount of work required is of order \(n^{4/3}\). This is an improvement on previous methods where the order is \(n^ 2\).